An operator approach for modelling the interdependence between the soil water boundary wetting and drying curves

In this study the relationship between two families of pairwise associated functions, describing boundary wetting and drying curves, is modelled. This relationship includes both regular and random constituents, and it is represented by a limited dataset of N known pairs of these curves, which pertain to N different soils. Using the dependent domain theory of hysteresis, we show that the regular constituent in this relationship can be described by a linear integral operator that, for a given input measured boundary wetting curve, predicts its associated boundary drying curve. The operator is optimized to reduce the influence of the random scattering of the pairs of curves. The optimization of the operator is performed with respect to the given input measured boundary wetting curve using a representative calibration dataset of k (k≤N) pairs of curves, which are a part of the N available measured pairs. The optimized operator should satisfy two opposite conditions: (i) the best possible accuracy at reproducing the boundary drying curves used for operator optimization, and (ii) the least possible sensitivity with respect to excluding any one pair from the calibration dataset. We also apply the suggested modelling approach for derivation of the inverse operator model that predicts the boundary wetting curves from their associated measured boundary drying curves, with possibility of verification of the predictive reliability. The predictive performance of both operator models is mainly good, and their reliability can be permanently enhanced by updating them with new incoming measured data.